How to select vertices on different meshes in edit mode
Joining

Tab out of Edit Mode, select one mesh, Shift select the other, and key Ctrl + J to join them. Tab back into Edit Mode.



Shading

If the shading does not look weird (darker) on one or both of the meshes, ignore the following paragraph.

Select one vertex of the weird one(s) and key Ctrl + L to select the rest of it(them). Key T to toggle open/close the Toolshelf, go to the Shading/UVs tab, and click on the Recalculate button. Key A once or twice to deselect the mesh(es).



Bridging

Do read this paragraph.

Key Alt  and RMB while hovering over one of the edge loops. Do this for the other edge loop as well. This should select the whole loop. Key W to open the Specials pop up menu and select Bridge Edge Loops.